Fractional order PIλDμ controller design for satisfying time and frequency domain specifications simultaneously

• Published in: ISA transactions 2017-05, Vol.68, p.212-222
• Main Authors: Zheng, WeiJia, Luo, Ying, Wang, XiaoHong, Pi, YouGuo, Chen, YangQuan
• Format: Article
• Language: English
• Subjects: Differential Evolution algorithm; Fractional order PIλDμ controller design; PMSM servo system
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2017.02.016

In order to achieve a desired control performance characterized by satisfying specifications in both frequency-domain and time-domain simultaneously, an optimal fractional order proportional integral derivative (PIλDμ) controller design strategy is proposed based on analytical calculation and Differential Evolution algorithm for a permanent magnet synchronous motor (PMSM) servo system in this paper. In this controller design, the frequency-domain specifications can guarantee the system stability with both gain margin and phase margin, and also the system robustness to loop gain variations. The time-domain specifications can ensure the desired step response performance with rapid rising curve, constrained overshoot, and proper power consuming. Compared with the PIλ controller and the traditional PID controller, PIλDμ controller can get obvious benefits from two more degrees of freedom of the fractional orders λ and μ on satisfying multiple constraints simultaneously and achieving better servo tracking performance for the PMSM servo system. PMSM speed tracking simulations and experiments are demonstrated to show the significant advantages of using the proposed optimal PIλDμ controller over the optimal fractional order PIλ controller and traditional integer order PID controller. •Based on the differential evolution algorithm, the tuning method proposed in the manuscript combines the requirements in both frequency domain and time domain. Therefore, the obtained PIλDμPIλDμcontroller achieves both the robustness to gain variations and the optimal dynamic response performance.•The gain margin specification, which is always ignored in the frequency-domain method, is introduced as the boundary condition for the tuning method. Therefore, the system stability with gain and phase margin is guaranteed.•The obtained controller satisfies multiple constraints simultaneously and achieves much better servo tracking performance for the PMSM servo system over the optimal fractional order PIλPλ controller and the traditional order PID controller.